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Flow-shop scheduling problems are generally studied in a single-objective deterministic way whereas they are multiobjective and are subjected to a wide range of uncertainties. Although evolutionary algorithms are commonly used to solve multiobjective and stochastic problems, very few approaches combine simultaneously these two aspects. In the paper the multiobjective flow shop scheduling problem is modeled with the stochastic processing time and the machine breakdown. A mathematical scheme is designed for the largest flow of time and the largest delay time. A hybrid multiobjective genetic algorithm is proposed to solve the optimization problems iteratively on uncertain condition. The results of simulation experiments are shown that the algorithm can provide a good performance for the flow shop scheduling problems on the uncertain condition.